A362472 E.g.f. satisfies A(x) = exp(x + x^3 * A(x)^3).

1, 1, 1, 7, 97, 961, 10201, 177241, 3801505, 80718625, 1887205681, 52896262321, 1648697978401, 54216677033377, 1928791931034697, 75326014326206281, 3159713152034201281, 140373558362282197441, 6632746205445950124385, 333591744669464008432225

Offset

0,4

Links

Seiichi Manyama, Table of n, a(n) for n = 0..384

Eric Weisstein's World of Mathematics, Lambert W-Function.

Formula

E.g.f.: exp(x - LambertW(-3*x^3 * exp(3*x))/3) = ( -LambertW(-3*x^3 * exp(3*x))/(3*x^3) )^(1/3).

a(n) = n! * Sum_{k=0..floor(n/3)} (3*k+1)^(n-2*k-1) / (k! * (n-3*k)!).

Prog

(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-lambertw(-3*x^3*exp(3*x))/3)))

Crossrefs

Column k=6 of A362490.

Cf. A143768, A349562, A362473.

Cf. A362392, A362481.

Sequence in context: A219088 A116261 A289851 * A242377 A178005 A268706

Adjacent sequences: A362469 A362470 A362471 * A362473 A362474 A362475

Keyword

nonn

Author

Seiichi Manyama, Apr 21 2023

Status

approved